Since these events took place, theoreticians and geometers alike have not been idle. Among their many findings, for the sake of this chapter we underline the (nowadays) well understood fact that the affine connection can be split, in general, into three pieces, namely, curvature, torsion, and non-metricity, each with its own physical interpretation: the rotation of a vector transported along a closed curve, the non-closure of parallelograms when two vectors are parallely transported along each other, and the variation of a vector's length when parallel-transported. It turns out that, when the action of the gravitational theory is built upon the lowest scalar of each of these pieces (thus switching off the other two), the resulting dynamical equations are precisely the Einstein ones [1]}. Diffemorphism and Lorentz invariances are preserved, and the background solutions of each formulation of GR turn out to be the same in such a way that it is only at the level of their respective boundary terms (relevant for some applications) that they can be distinguished from each other. Such three versions are called (canonical) GR, the teleparallel equivalent of GR [2]}, [3]}, and the (symmetric) teleparallel GR [4]}, [5]}, respectively. Fully enlarging GR to include non-vanishing contributions of every such piece of the affine connection yields a theory called metric-affine gravity, given by a triplet \(\lbrace \mathcal {M},g,\Gamma \rbrace \)  with a priori unspecified relations between \(g\)  and \(\Gamma \) . Such a theory contains not only the three equivalent formulations of GR on its corresponding limits, but also other gravitational theories explored in the literature such as Einstein-Cartan, Weyl gravity, etc. Such a picture can be very well dubbed as affinesiaCredit to Jose Beltrán Jiménez who, as far as we know, is the person to be blamed for coining this term..
